The disclosure relates to an acoustic method and device for localized, contactless, measurement of elastic and dissipative non-linearities and dynamic non-linear viscoelasticity in a medium subjected to a low-frequency acoustic stress and probed by ultrasonic pulses or wave trains. A device for measuring elastic and dissipative nonlinearities and viscoelasticity of a specimen includes an emitter for transmitting a low-frequency acoustic wave and a receiver to receive said low-frequency acoustic wave, which is capable of creating a low-frequency periodic variation of a hydrostatic pressure in the specimen; a generator to generate high-frequency ultrasonic pulses and a receiver to receive said pulses; and an analysis unit that includes a model for calculating modulations in time of flight and in amplitude of the ultrasonic pulses that are induced by the low-frequency acoustic wave passing through the specimen to quantify the elastic and dissipative non-linearities and the non-linear viscoelasticity of the specimen.
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